Skyscrapers and Harmonic Motion
The John Hancock Tower is one of
the tallest skyscrapers in
New England. This 60-story
building is 240.7 meters (790 feet)
tall and was completed in 1976. With
10,344 windowpanes, the most
striking feature of this building is
that it is completely covered in glass!
While this skyscraper was being
built in 1972 and 1973, a disaster
struck—windowpanes started falling
out from all over the building and
crashing to the ground. So many fell
out that, with the boarded up window
holes, the Hancock Tower was
nicknamed the “plywood palace.”
Some people said the windows fell
out because the building swayed too much in the wind—they
thought the problem was due to the natural harmonic motion of the
skyscraper.
Why does a skyscraper sway?
Just like trees which experience harmonic motion in strong winds,
skyscrapers also sway side to side. Skyscrapers or any buildings,
even though made of steel and concrete, begin to vibrate when the
wind blows or an earthquake occurs. All buildings have a
fundamental frequency of vibration. For example, the fundamental
frequencies for buildings range as follows: 10 hertz for one-story
buildings, 2 hertz for a three- to five-story buildings, 0.5 to 1 for tall
buildings (10 to 20 stories high), and 0.17 hertz for skyscrapers.
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On the top floor of some skyscrapers, with a strong wind, the
amplitude of their side-to-side motion (“sway”) can be several feet.
Therefore, engineers have carefully designed skyscrapers to handle
a large swaying motion. Engineers strive to keep the amplitude very
small so that the people inside will not be disturbed. When the
falling windowpanes of the Hancock Tower were blamed on the
building’s sway, engineers were quick to point out that the John
Hancock Tower was designed to sway slightly. Engineers did not
think the sway of this building was causing the falling windows.
Swaying is a form of simple harmonic motion. Swaying starts with
a disturbing or force such as the wind pushing on the side of the
building. A restoring force keeps the motion always accelerating
back towards its equilibrium point. In a skyscraper, the equilibrium
point is when the building is perfectly straight. For a skyscraper, the
restoring force is provided by the mass of the structure of the
skyscraper. The Hancock Tower has a stiff backbone made up of
steel columns and beams in the skyscraper’s core. That extra
sturdiness allows the building to bend slightly and then ease back
towards its center point. Some skyscrapers get their restoring force
from hollow, rigid tubes at the perimeter of the structure. The
advantage of the tubes is that they are a strong core design, with
less weight.
The Citicorp Center in New York
City was the first building to
have a mechanical means for
providing a restoring force to
counteract swaying. A 410-ton
concrete weight housed on the
top floors of the building slides
back and forth in opposition to
the sway caused by wind. Thus,
the restoring force in the Citicorp
Center is accomplished by
CHAPTER 19: HARMONIC MOTION
shifting the center of mass of the
building so that gravity pulls the
building back towards its
“straight” or equilibrium position.
The device used in the Citicorp
Center is called a windcompensating damper or “tuned
mass damper.”
William LeMessurier, an
innovative engineer, installed the
tuned mass damper in the Citicorp
Center. LeMessurier was also
involved in installing a tuned mass damper in the Hancock Tower.
This device wasn’t necessary to stop windows from falling, but was
used to keep the building from twisting as it swayed — a very
disturbing affect felt by the people on the top floors of the building.
The reason for the falling windows
The windows of the Hancock Tower fell out because of how the
double-paned glass was bonded to the window frame. The bonding
prevented the glass from responding to temperature changes and
wind forces. Because the windows were held too rigidly by the
bonding, the glass fractured easily and fell out. The modern John
Hancock Tower sways slightly in the wind just like before, but
without twisting thanks to the tuned mass damper. Also, the
bonding of the windows has been fixed, and now the windows stay
in place.
What is the tallest building in the world?
The current world champion of skyscrapers (2004) is Taipei 101
located in Taiwan. It is 508 meters tall (1,667 feet) with 101 floors
above ground. Since both earthquakes and wind are concerns in
Taiwan, the building’s engineers took extra precautions. The 800ton wind-compensating damper at the top of the building is a large
spherical shape hung as a simple pendulum. The damper is visible
to the public on the 88th and 89th floors where there is a restaurant!
When the building begins to sway either due to wind or an
earthquake, the damper acts as a restoring force. The Taipei 101 is
built to withstand an earthquake greater than 7 on the Richter scale!
Other countries are currently constructing skyscrapers that will be
even taller than Taipei 101. So, this world record holder will not be
the tallest building for very long. With modern materials, and future
innovations yet to come, the main limitation to the height of future
skyscrapers is the cost to build such tall buildings!
Questions:
1. From the reading, why were the windows falling out of the
John Hancock Tower?
2. Describe the sway of a building. Use the terms force and
harmonic motion in your answer.
3. Research and write a brief report about William LeMessier’s
work on the Citicorp Center.
4. Research the John Hancock Tower and find out what its
tuned mass damper looks like and how it works.
5. Find out why Taipei 101 “beats” the Sears Tower as the
world’s tallest building.
UNIT 7 VIBRATIONS, WAVES AND SOUND
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